Dot Product and Angle in Degrees between two Numpy Arrays

Question

I would like to write a function that takes two numpy arrays with the same length and returns:

• the dot product of the two arrays
• the angle between the two vectors in degrees

The expected output is as such:

print(angle_dot(np.array([0., 1.]), np.array([1., 0.])))
## (0.0, 90.0)

print(angle_dot(np.array([2., -1, 1, -2]), np.array([-1., 1.5, 3., 1])))
## (-2.5, 102.5)

This is what I have so far, I can't seem to get the value for the angle between the arrays correct.

import numpy as np
def angle_dot(a, b):
    dot_product = round(np.dot(a, b), 1)
    angle = round(np.degrees(dot_product), 1)
    return dot_product, angle

print(angle_dot(np.array([0., 1.]), np.array([1., 0.])))
## (0.0, 0.0)

print(angle_dot(np.array([2., -1, 1, -2]), np.array([-1., 1.5, 3., 1])))
## (-2.5, -143.2)

Answer 1

The angle is defined using this formula (this is just one way of defining it):

cos(alpha) = (a . b) / (|a| * |b|)

So, the angle is:

alpha = arccos((a . b) / (|a| * |b|))

Code:

import numpy as np

def angle_dot(a, b):
    dot_product = np.dot(a, b)
    prod_of_norms = np.linalg.norm(a) * np.linalg.norm(b)
    angle = round(np.degrees(np.arccos(dot_product / prod_of_norms)), 1)
    return round(dot_product, 1), angle

print(angle_dot(np.array([0., 1.]), np.array([1., 0.])))

print(angle_dot(np.array([2., -1, 1, -2]), np.array([-1., 1.5, 3., 1])))

Output:

(0.0, 90.0)
(-2.5, 102.5)